The overall objective of this grant is to continue to develop and apply statistical methods in AIDS research. With over 150,000 AIDS cases reported to the Centers for Disease Control as of October 1990, the AIDS epidemic is one of the most urgent public health problems in the United States. The focus of this research is on statistical modeling of the AIDS epidemic. There are three specific objectives of this proposal. The first is to develop statistical methods for obtaining improved estimates of current HIV prevalence .and future AIDS incidence. Methods will be investigated for combining AIDS incidence data and incubation distribution estimates with direct estimates of HIV prevalence obtained from epidemiologic surveys. The second objective is to develop a statistical framework for analyzing serial HIV prevalence surveys and to determine what information can be gleaned about the incidence of HIV infection from such data. The methods will be applied to military applicant screening data in the U.S. The third objective is to carefully study the uncertainties which may effect the back-calculation methodology and how these uncertainties are propagated into the estimates of current and past HIV prevalence, and projections of future AIDS incidence. The sources of uncertainty that will be considered include the parametric mode-1 for the infection rate, the incubation period distribution, reporting delays and errors in AIDS incidence, and the efficacy and availability of treatment. This work will entail detailed sensitivity analyses and quantification of the effects of model misspecification. We will characterize the performance of back-calculation methods In a wide range of situations.